To bind a function that takes parameters, use an anonymous function to act as a closure over the parameters.

jQuery(function($) {
var param = 'text';
$('#textbox').click(function() {
EventWithParam(param);
// or just use it without calling out to another function
$(this).text(param);
});
});

Your example is executing the EventWithParam function, and then trying to bind to the result of that function call.

Calling unbind without specifying a function will unbind all handlers for the specified type of event (including the anonymous function). If you want to unbind that function specifically, you'll need to provide it with a name, like this:

jQuery(function($) {
var param = 'text',
clickCallback = function() {
EventWithParam(param);
// or just use it without calling out to another function
$(this).text(param);
};
$('#textbox').click(clickCallback);
});